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In the "Play" phase of Cribbage (31's), what is the optimal leading card to play. I have always played a 4 if I had one, because it can't be fifteened and is less likely to result in a run, because an opponent is unlikely to play a 5 or a 6. It is also not as useful as 1s, 2s or 3s at the later part of the Play when it gets close to 31.

However, I fear that this tactic is becoming too predictable, and my fellow players will know that my hand lacks a 4 if I have not played it immediately as a Leading card.

4 Answers
4

Having spent some time trying to work out probabilities and carrying out some research, I have come up with a few conclusions.

Almost NEVER lead with a 5 or a 10.

There are 16 cards that value 10 in the pack (30%), so playing a 5 gives a very high probability that the other player will get 2points for 15.

Same theory for leading with a 10. Although far fewer 5s are in the pack, these are highly valuable cards and often not sent to the crib.

Keep back Aces for the end

They come in very useful for getting 31 for 2, and possible doubles or triples.

6s, 7s, 8s, 9s

These are strong cards in a hand, so are often quite easy to 15. Leading with a 9 or 6 allows the other player to get a 15 with little worry of a run occurring. 7s and 8s can trick the other player into going for a 15 to gain you a run, but can be followed by another card to make a further run from the other player. This would give the other player 7 points and you 3 points. Not a great return.

Deuces and Treys

2s and 3s are what is left. A 2 is probably useful to hold back for the same reason as the Aces, but 2s and 3s are the safest options for leading.

So, the answer to vary the leading card (i.e. instead of always playing a 4) is to use a 3, or even possibly a 2.

Excellent list, i have thoughts though. 1) Never is too strong a word, it's acceptable to lead a 5 or 10 if you're prepared to pair what the other player uses to make a 15. It's probably a stronger move to lead a 10, because there are four kinds of 10 and therefor harder to pair. 4) Fours are also excellent to lead. The strength of 2-4 is that they cannot immediately turn into points off a 15 for the other player.
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TychoOct 25 '10 at 2:44

Points noted in my answer. I agree with 4, that is the card I always use, I wanted to find something less predictable. That is why 4 was left out of the answer. I have updated to make this clearer though.
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CodemwnciOct 25 '10 at 6:26

4's and 3's are my usual lead, if I have them. Then 8's and 9's.
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aramisJan 21 '12 at 9:04

If I have 2 cards that add to 5, I like to lead with one of those
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Sam I amFeb 27 '14 at 22:33

The first of a pair, or the middle card of a run

The key strategy to take away is that in the play you're trying to trap or entice the other player into playing something that might give them points but sets you up to get more, or you're trying to increase the number of cards they can play that will enable you to respond with a scoring play. For example:

If I have a pair, I typically lead with one of them.

You're hoping to entice the other player to play a pair-for-two so you can turn around and play triples for 6. An obvious exception is starting with a 5, as you're asking for them to take 15-2. Starting with a 10 is less risky as there are only four 5s in the deck but many 10-value cards.

The probability of the opponent getting dealt exactly 1 of the other cards of my pair is 23% (in their opening hand, they could have dumped it to the crib), while the probability of the opponent having both of the other cards of my pair is less than 1%.

If I have a run I'll also often play the middle card. That gives me run-for-3 options if they play any one of four cards, the two ranks below and the two ranks above what I played. For example, if I have 6, 7, and 8 I'll play the 7. If they play 6 and I can play 8 run-for-3; 5 I play 6, 8 I play 6 and 9 I play 8. This particular run also had the advantage of trapping them into playing the 8 to get 15-2, where you can answer with a run-for-three. I know it's only a one point advantage, but I've won many a game by one point.

Of course if you have 6-7-7-8 then you can do both strategies simultaneously and you're really set, both for the play and for the killer hand you're about to lay down during the show. :)

Appendix:

To compute the probability of my opponent getting dealt exactly 1 of the other 2 cards of my pair is (in octave or matlab code):

This strategy is nice, but it should be noted that the first bullet is a move where you will probably very rarely see pay off. The chances of having three cards of one value spread between two four-card hands are (though I'm no mathematician) quite slim, I imagine.
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IsziJan 4 '11 at 15:24

1

Good point although in practice I'd say I see this happen every couple of games or so (at least until the people you play with wise up and stop playing into your strategy). I think the reason it happens more than probability theory would lead you to expect is that certain cards are more valuable and thus more likely to be kept in the hand vice sent to the crib. For example, 5s, Jacks, 7s and 8s. Those cards are good for making 15s and with 7 & 8 are in the wheel house for runs.
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Adam WuerlJan 4 '11 at 19:18

@izzy pretty slim, but I've seen some ugly hands happen. to have a hand of a pair in yours and a single in theirs is actually not that low. I'm to tired to do the branching probabilities, and don't know the shortcut math, but it's better than 1/5525, as that's the odds of 3 5's happening in the first 3 cards dealt...
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aramisJan 21 '12 at 9:24

On occasion, there may be value in playing a card of the same rank as that turned up in the cut, since there's a reduced chance of your opponent being able to pair it. "See one, play one", was how it was usually described. I wouldn't recommend it for a 5, though...

Actually, see one, play one is not so good for 6-9, as they have complements that are not evidenced. For 6,7,8,9 showing, playing the complement in reduced chance of a 15, but... no reduction in odds for the mate. And leading a 5 is a desperation move.
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aramisJan 21 '12 at 9:28

A great deal of leading off in the play depends on the board position. If you are ahead, you should play defensively, so playing a 4 is fine there, and any low card (1-4) could be counted. It is a common mistake to be tied to closely to your aces, as they usually only get you a point for go, and very rarely a 31.

If you are behind, playing from pairs, playing connected cards etc, hoping to get points after they get points is a common strategy. so if you have a horrible hand and are behind (A79Q), you would lead the 7, hoping they play 8 for 15-for-two, and you can play 9 for 24-for-three.

Playing a 5 can be a fun play in certain situations (you have a 5JQK hand, and you only need two points to win, play the five, and you have a 75% chance of matching their 15), but is quite bad in most others. Playing a 10 is not too bad, especially if it is a double (no chance for them to redouble for 12), and that same principle is true for all cards 8 and up, there is no danger if they match your card.